GRACEFUL CHROMATIC NUMBER OF THE FAMILY OF CENTRIPETAL GRAPH

  • Deninta Dwi Ayu Lestari(1)
    Universitas Jember
  • Arika Indah Kristiana(2*)
    University of Jember
  • Rafiantika Megahnia Prihandini(3)
    Universitas Jember
  • Ridho Alfarisi(4)
    Universitas Jember
  • Toto Bara Setiawan(5)
    Universitas Jember
  • Robiatul Adawiyah(6)
    Universitas Jember
  • (*) Corresponding Author
Keywords: Chromatic Number, Graceful Coloring, Centripetal Graph

Abstract

One of the topics studied in graphs is graph coloring. The definition of a graceful coloring, namely $k$-elegant coloring of a graph G is the exact vertex coloring c:V(G)→{ 1,2,...,k} where k≥2 induces the exact vertex coloring c^': V(G)→ {1,2,...,k-1} which is defined by c(uv)=|c(u)-c(v)|. The exact vertex coloring c of a graph G is a graceful coloring if c is a k-elegant coloring for k∈N. The graceful chromatic number is the minimum k value where graph G has k-elegant coloring, the elegant chromatic number of graph G is denoted by X_g (G). This article will discuss graceful chromatic numbers in the centripetal graph family which includes octopus graph (O_n), sandat graph (St_n),dutch windmill graph (D_3^m) , and a volcano graph (V_n).

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Published
2024-02-09
How to Cite
1.
Lestari D, Kristiana A, Prihandini R, Alfarisi R, Setiawan T, Adawiyah R. GRACEFUL CHROMATIC NUMBER OF THE FAMILY OF CENTRIPETAL GRAPH. JD [Internet]. 9Feb.2024 [cited 16Apr.2024];6(1):57-4. Available from: https://ejurnal.undana.ac.id/index.php/JD/article/view/12746
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Articles